## Research Seminars in the School of Mathematical Sciences

The School of Mathematical Sciences host regular research seminars delivered by internal and external researchers on topics across mathematical sciences. Seminars take place on the Kevin Street campus and are open to all.

## Seminar 6/10/17: Formation and Growth of the first Black Holes

Formation and Growth of the first Black Holes

John Regan

Dublin City University

Friday 6 October 2017

1pm, Blue Room, 4th floor, Main Building, DIT Kevin Street

Abstract:

The discovery of supermassive black holes (SMBHs) at high-z (z ≥ 6) is a direct challenge to our understanding of the formation of the structure at small scales in the Universe (first stars, galaxies and black holes). The first stars are expected to form in mini-haloes where a combination of gravity and gas chemistry result in the first runaway collapse. These first stars may be massive with characteristic masses in the region of 50 Msolar. However, the observations of SMBHs with masses of 1 billion solar masses shortly after when we expect the first stars to form is perplexing.

I will discuss possible solutions to this problem. In particular I will discuss forming unusually massive stars in the early Universe which could explain the high-z SMBHs and also importantly the growth requirements subsequently (from either PopIII stars or supermassive stars) – which will likely require periods of super-critical growth.

## Seminar 31/03/17: Geometric aspects of fluid models with vorticity

Geometric aspects of fluid models with vorticity

Tony Lyons

Waterford Institute of Technology

Friday 31 March 2017

4pm, Room KE2-008, 2nd Floor, Main Building, DIT Kevin Street

Abstract:

In this talk we outline a derivation of a two-component system of nonlinear PDE modelling shallow water-waves with vorticity. In line with several other well known shallow water models with quadratic nonlinearities, such as the Camassa-Holm and Hunter-Saxton equations, we show how this may be interpreted as a geodesic flow on an appropriate diffeomorphism group. We then outline how this geometric interpretation may be used to show the well-posedness of the fluid model, and establish criteria for the existence of global solutions for the system.

## Seminar 31/03/17: Integrable nonlocal multi-component equations with PT and CPT symmetries

Integrable nonlocal multi-component equations with PT and CPT symmetries

Georgi Grahovski

University of Essex

Friday 31 March 2017

2.30pm, Room KE2-008, 2nd Floor, Main Building, DIT Kevin Street

Abstract:

We will present extensions of N-wave and derivative NLS types of equations with PT and CPT-symmetries. The types of (nonlocal) reductions leading to integrable equations invariant with respect to *C-* (charge conjugation), *P-* (spatial reflection) and *T-* (time reversal) symmetries are described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived.

Based on examples of 3-wave (related to the algebra *sl(3,C)*) and 4-wave (related to the algebra *so(5,C)*) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters. Furthermore, we will present multi-component generalizations of derivative nonlinear Schrodinger (DNLS) type of related to A.III symmetric spaces and having with CPT-symmetry. This includes equations of Kaup-Newell (KN) and Gerdjikov-Ivanov (GI) types.

## Seminar 31/03/17: Breeding new methods for finding first order saddle points

Breeding new methods for finding first order saddle points

Carlos Argáez

University of Iceland

Friday 31 March 2017

3.30pm, Room KE2-008, 2nd Floor, Main Building, DIT Kevin Street

Abstract:

The minimum mode following method for finding first order saddle points on an energy surface is used, for example, in simulations of long time scale evolution of materials and surfaces of solids. Such simulations are increasingly being carried out in combination with computationally demanding electronic structure calculations of atomic interactions, so it is essential to reduce as much as possible the number of chemical-function evaluations needed to find the relevant saddle points. Several improvements to the method are discussed here. Among the new advantages of this method, minimization method is used here: the minimum mode is estimated using the Davidson method with a new coupling on the Hessian approximation. Significant savings in the number of function evaluations can be obtained by assuming the minimum mode is unchanged until the atomic displacement exceeds a threshold value. In total, with this new breed the number of function evaluations is reduced to less than a third with the improved method as compared with the best previously reported results.

## Seminar 31/03/17: Modelling of the stratified flow circulation in Greenland fjords

Modelling of the stratified flow circulation in Greenland fjords

Violeta Moloney

Swansea University

Friday 31 March 2017

2pm, Room KE2-008, 2nd Floor, Main Building, DIT Kevin Street

Abstract:

The glacier/fjord/ocean is a unique complex system. The seasonal changes in atmospheric temperatures and constant interaction with ambient waters affect the salinity and temperature balance in the fjords and that has an impact on the glacier melt rate. The subject of investigation is the physical processes in Sermilik Fjord, Greenland.

This research investigates the effects of the subglacial discharge, Coriolis force, wind and tidal forcing on the stratification and circulation in the fjord using the three-dimensional model TELEMAC-3D. Firstly, in order to avoid large horizontal pressure gradients at an open boundary, the matching conditions for temperature and salinity between coastal and fjord domains had to be found before the other forces such as wind, tide and fresh water discharge were applied. Secondly, measured wind speed, tidal levels and velocities, and a representation of the subglacial discharge have been implemented to reproduce an analysis of seasonal conditions. After calibration, the tidal model produced matching results with the measured tides. The tidal analysis shows that the strength and direction of the tidal currents are sensitive to any changes in the width and shape of the domain. The effect of Coriolis force, the wind stress and the tidal propagation has been shown to play an important role on the fjord circulation, and particularly the stratification. However, the wind forcing has the strongest effect on the velocities, temperature and salinity profiles through the water column. The addition of the subglacial discharge has produced the turbulent flow that affects stratification near the glacier front, but it has little effect on the fjord dynamics further away from the source. When all forces are combined the winter conditions have shown the biggest changes in the fjord dynamics, as strong winds drive the circulation in fjord and that in turn delivers the coastal waters to the glacier.